Award-Winning Test Prep & Academic Tutoring in Clifton Park, NY

"The student has a test Thursday. We went over some of the problems she might encounter. I will be sending her some more to practice. "

"Today's session was a review of the material we covered in our last session and extended into thinking critically about the material. Our focus today was on the student's homework - identifying which of the 5 theorems for parallel lines were being used and then solving for an unknown angle/ variable. From the beginning of our session with the practice problem from last session to the end of our session with the "thinking critical" questions, he was very actively engaged and was guiding me through problems or giving me answers with confidence. He has a test Monday and he assured me that he thought the current material was easy - a very positive attitude! He was also able to quickly correct himself whenever he noticed a mistake. I've noticed that sometimes there may be slight questions when trying to solve for x in terms of order of operations, but that may be easily ironed out with some practice problems during our next session. I left him with 10 practice problems on identifying pairs of angles - a little more practice before his test. Some were slightly more challenging than others, but after today's session, I believe he'll be able to complete them all correctly. "

"We began the session by reviewing the steps for graphing rational functions. I broke the method down into six steps. The first step involved factoring the numerator and denominator of the rational function. This step is necessary because cancellation of terms is the basis for finding the "holes" of the function which is the second of the six steps. I highlighted the fact that once terms were cancelled, we would analyze the behavior of what remained. We learned to find the vertical asymptotes by analyzing the denominator of the function and the horizontal asymptotes by considering the end behavior of the functions (we focused on the three main cases). We also discussed slant asymptotes which exist in special cases. The fifth step was finding the x and y intercepts. The last step involved using the results of all the previous steps to sketch the function. She was very adept at applying the algorithm. For the remainder of the session, we discussed the characteristics of exponential and logarithmic functions, how to convert between the two forms, and some basic methods of solving both types of equations. Here, I highlighted the fact that exponents and logarithms were inverse operations, similar to addition/subtraction and multiplication/division which would make itself more obvious when we began to learn solving methods. We saw that the parent exponential function did not have a restricted domain but did have a restricted range and because the parent logarithm function is the exponential inverse, the opposite was true for it. We learned the properties of logarithms by deriving them from the familiar properties of exponents. We practiced converting an equation from exponential form to logarithmic form and vice-versa. Lastly we discussed some equation solving methods. These methods included form conversion, matching exponents of equal bases, and exponentiating/logging both sides of the equation. "

"We went over the student's final review sheet on coplanar points, collinear points, and how to find the distance between two points using Pythagorean's Theorem. I showed him how to solve and simplify square roots and gave him many practice problems until he understood it. I stressed that he practice his math and Spanish every night until his final!"

"The student reviewed 2-digit x 3-digit multiplication as well as division with 2-digit divisors without remainders. She has the concepts down, but is still hesitant with the basic multiplication table. As we go forward, we will begin each session with a quick multiplication 'fast math.' She is working on decimals and rounding. We worked on identifying place value from millions to hundredths. She completed her homework of rounding to the hundredths and she did very well. "

"We reviewed a series of homework problems (20), which involved adding and subtracting complex fractions with single or multiple variables. This involved identifying common denominators and converting fractions. We also substituted the result we identified to confirm that it was correct."

"The student and I went over the new topics covered in her chemistry class, which included balancing chemical reactions of chemical compounds. She did several practice problems of different reactions, such as decomposition metal chlorates, hydroxides, carbonates, and single and double displacement reactions. With more practice, she will be more used to working with polyatomic ions. "

"The student and I continued working on circles. This time the focus was on finding arc lengths given an outside angle and vice versa. Her book did a good job of applying this concept to more complex problems so she could see that what looks complicated is just using the same theorem. I encouraged her to commit the theorems to memory to ensure she's ready for upcoming tests and quizzes."